Terao's conjecture for triangular arrangements

Jean Vallès (1) , Simone Marchesi (2)

1 UPPA - Université de Pau et des Pays de l'Adour
2 UNICAMP - Universidade Estadual de Campinas = University of Campinas

In this work we study line arrangements consisting in lines passing through three non aligned points. We call them triangular arrangements. We prove that any of this arrangement is associated to another one with the same combinatorics, constructed by removing lines to a Ceva arrangement. We then characterize the freeness of such triangular arrangements, which will depend on the combinatorics of the deleted lines. We give two triangular arrangements having the same weak combinatorics (that means the same number $t_i$ of points with multiplicity $i, i\ge 2$), such that one is free but the other one is not. Finally, we prove that Terao's conjecture holds for triangular arrangement.

Domaines: Géométrie algébrique [math.AG]; Combinatoire [math.CO]; Topologie algébrique [math.AT]

Jean Vallès, Simone Marchesi. Terao's conjecture for triangular arrangements. 2019. ⟨hal-02074118v2⟩